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mon·o·ton·ic Mathematics. Designating sequences, the successive members of which either consistently increase or decrease but do not oscillate in relative value. Each member of a monotone increasing sequence is greater than or equal to the preceding member; each member of a monotone decreasing sequence is less than or equal to the preceding member.

So actually I was a bit off beam since monotonic seems to include equality. But that's not how I remember it . . . . .